Cohomology of class groups of cyclotomic fields; an application to Morse-Smale diffeomorphisms

Abstract

The obstruction group SSF came up in the topological investigations of Shub and Franks. It was studied by Bass and Lenstra; the latter showed that

$$\text{SSF}\text{≅}\text{⊕}\text{n⩾1}\text{Pic}\text{Z}\text{ζ}{}_{\mathrm{n}}\text{,}\text{1}\text{n}$$

. In this paper the structure of SSF as an abelian group is determined. It is proved that

$$\text{SSF}\text{≅}\text{⊕}\text{n⩾1}\text{Z}\text{⧸/n}\text{Z}$$

confirming a conjecture of Lenstra.